The position vector of a particle is given
by r = 3ti +5t^2j+7k. Find the direction in
which the particle experiences net force?
Answers
Answer:
wseNotessearch
Search for any book or any question
Physics Questions and Answers
MENU
The position vector of a particle is given by r(t)=t^3*i+t^2*j. What are it's velocity speed and acceleration when t=2
print Print document PDF list Cite
Expert Answers info
TUSHAR CHANDRA eNotes educator | CERTIFIED EDUCATOR
We have the position vector given in terms of time t. r(t) = t^3*i + t^2*j
To find the velocity vector we have to differentiate r(t) with respect to time.
r'(t) = 3t^2*i + 2t*j
The vector representing acceleration is the derivative of the position vector
r''(t) = 6t*i + 2*j
When time t = 2.
The velocity vector is 3*2^2*i + 2*2*j
=> 12*i + 4*j
The speed is the absolute value of the velocity vector or sqrt(12^2 + 4^2) = sqrt (144 + 16) = sqrt 160
The acceleration vector is 6*2*i + 2*j
=> 12*i + 2*j
The required acceleration at t=2 is 12*i + 2*j and the speed is sqrt 160. ok follow me
Answer: a=10j^
Explanation: v=dr/dt
(.'. r=3ti^+5t^2j^+7k^)
v= d/dt*3ti^ +d/dt*5t^2j^ +d/dt*7k^
dr/dt=3i^+10tj^
accleration of the object
a=dv/dt=d^2r/dt^2
a=10j^